For the closed-loop system with plant model and controller given by
G(s) = (s2+81)/(s2(s2 + 100)) D(s) = (K (S+1))/(S+13)
(a) Find the locus of the closed-loop roots (poles) with respect to K;
(b) Is there a value of K that will cause all roots to have a damping ratio greater than 0.5?
(c) Find the values of K that yield closed-loop poles with the damping ratio ?
(d) Use Matlab to plot the response of the resulting design to a reference step input.